The \(T=0\)  Random Field Ising Model is a prototype model for the study
of collective phenomena in disordered systems. Although it neglects
thermal fluctuations, it contains essential competitions between the
quenched disorder, the ferromagnetic interaction and the external
applied field. The model can be numerically studied from two
different points of view: on the one hand, the exact ground state
calculation [1]}, [2]}, [3]}, [4]}
provides an approach to the
equilibrium phase diagram. On the other the use of a local relaxation
dynamics based on single spin-flips provides a good framework for the
understanding of avalanche dynamics and hysteresis
[5]}, [6]}, which is closer to experimental
observations. In this sense, the model is a good workbench for the
comparison of equilibrium and out-of-equilibrium trajectories.
